Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 17 Aug 2009
Posts: 216

If x and y are integers and y = x + 3 + 4  x, does y equal 7? [#permalink]
Show Tags
29 Jan 2010, 11:55
7
This post was BOOKMARKED
Question Stats:
69% (01:22) correct 31% (01:27) wrong based on 860 sessions
HideShow timer Statistics
If x and y are integers and y = x + 3 + 4  x, does y equal 7? (1) x < 4 (2) x > 3
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 27 Jul 2015, 14:57, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



CEO
Joined: 17 Nov 2007
Posts: 3525
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: If x and y are integers and y = x + 3 + 4  x, does y equal 7? [#permalink]
Show Tags
29 Jan 2010, 12:24
if x and y are integers and y= x+ 3 + 4x, does y equal 7If we carefully look at the question we can see that "does y equal 7" actually means that y doesn't depend on x and then you can see that if we open two moduli with same signs (++ or ), x and x disappear and 3+4 is 7. So, let's see when we can open moduli ++ or : ++) x>3 and x<4 or x e (3,4) ) x<3 and x>4  it can't be. So, if x between 3 and 4, y =7. Now, look at our statements: it is obvious that we need two statements. C.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame



Intern
Joined: 18 Aug 2010
Posts: 6

If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
26 Sep 2010, 21:26
3
This post received KUDOS
23
This post was BOOKMARKED
If x and y are integers and y = x + 3 + 4  x, does y equals 7? (1) x < 4 (2) x > 3
_________________
"Learning never exhausts the mind." Leonardo da Vinci



Math Expert
Joined: 02 Sep 2009
Posts: 44399

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
26 Sep 2010, 23:06
8
This post received KUDOS
Expert's post
8
This post was BOOKMARKED
thirst4edu wrote: If x & y are integers and y=x+3 + 4x, does y equals 7? 1) x < 4 2) x > 3 Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks. OA is \(y=x+3+4x\) two check points: \(x=3\) and \(x=4\) (check point: the value of \(x\) when expression in  equals to zero), hence three ranges to consider: A. \(x<{3}\) > \(y= x + 3 +4x =x3+4x=2x+1\), which means that when \(x\) is in the range {infinity,3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range); B. \(3\leq{x}\leq{4}\) > \(y=x+3+4x=x+3+4x=7\), which means that when \(x\) is in the range {3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range); C. \(x>{4}\) > \(y=x+3+4x=x+34+x=2x1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range). Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {3,4} (1) \(x<4\) > not sufficient (\(x<4\) but we don't know if it's \(\geq{3}\)); (2) \(x>3\) > not sufficient (\(x>3\) but we don't know if it's \(\leq{4}\)); (1)+(2) \(3<x<4\) exactly the range we needed, so \(y=7\). Sufficient. Answer: C. OR: looking at \(y=x+3+4x\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4x\) are both positive, in this case \(xes\) cancel out each other and we would have \(y=x+3+4x=x+3+4x=7\). Both \(x+3\) and \(4x\) are positive in the range \(3<{x}<4\) (\(x+3>0\) > \(x>3\) and \(4x>0\) > \(x<4\)). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Retired Moderator
Joined: 02 Sep 2010
Posts: 779
Location: London

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
26 Sep 2010, 23:09
5
This post received KUDOS
Let's first solve x+3+4x=7 to answer "when is this true ?" You can solve algebraically but it is much easier to do it using a simple number line approach. Remember xa means distance between x and a on the number line Here the two points in question are 3 and 4 Now it is easy to imagine the three cases that x is to the left of 3, between 3 and 4 and to the right of 4. The only case when the two distances add up to the distance between 3 and 4, ie, 7 is case two. In case 1 and 3, the sum will exceed 7 1) could mean case 2 or 3. Not sufficient 2) could mean case 1 or 2. Not sufficient 1+2) can only mean case 2. Sufficient to know that y=7 Answer is (c)
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 30 Aug 2010
Posts: 91
Location: Bangalore, India

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
27 Sep 2010, 00:47
2
This post received KUDOS
2
This post was BOOKMARKED
thirst4edu wrote: If x & y are integers and y=x+3 + 4x, does y equals 7? 1) x < 4 2) x > 3 Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks. OA is Guys, the be low is my approcah for any modulus qtn in GMAT. Remember. The meaning of xy is "On the number line, the distance of X from +Y" The meaning of x+y is "On the number line, the distance of X from Y" The meaning of x is "On the number line, the distance of X from 0". Qtn: for integers X and Y, If y=x+3 + 4x, does y equals 7 ==> is the SUM of the distance b/e x and 3 , and x and 4 equals to 7? ==> .........3......0...........4..... observe that X has to be anywhere b/w 3 and 4 or on any of these points for the total distance to be 7 Stmnt1: X < 4: Answer could be Yes if X is < 4 and b/w 3 and 4 but from the given information (i.e X<4) X could be some where left to 3 in which case the total distance would be > 7 hence insufficient. ......X....3......0..........4 answer to the qtn: NO or ............3...X...0.........4 answer to the qtn: YES Stmnt2: X > 3: Answer could be Yes if X is > 3 and b/w 3 and 4 but from the given information (i.e X>3) X could be some where right to 4 in which case the total distance would be > 7 hence insufficient. ..........3......0..........4...X... answer to the qtn: NO or ..........3...X...0.........4 answer to the qtn: YES 1&2 X must be b/w 3 and 4 ..........3.X.X.X...0.X.X.X.X.X...4...... answer is always YES..hence Sufficient. Answer C. Hope it helps



Manager
Joined: 06 Aug 2010
Posts: 201
Location: Boston

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
27 Sep 2010, 11:51
2
This post received KUDOS
thirst4edu wrote: If x & y are integers and y=x+3 + 4x, does y equals 7? 1) x < 4 2) x > 3 Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks. OA is Either choice by itself is clearly insufficient: (1) If x = 3, y = 3+3 + 43 = 7. If x = 100, then y = 97 + 104 = 201. (2) If x = 2, y = 1 + 6 = 7. If x = 100, then y = 103 + 96 = 199. Putting them together, you can quickly check every integer value of x from 3 to 4 and see that y = 7 for every one. It's only 6 values to check, you can do it very quickly in your head. (C)



Manager
Joined: 27 May 2010
Posts: 78

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
28 Sep 2010, 10:58
thanks bunuel. always great explanations!!



Retired Moderator
Joined: 05 Jul 2006
Posts: 1741

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
29 Sep 2010, 10:21
Bunuel rocks, cheers mate



Manager
Joined: 27 Dec 2011
Posts: 66

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
26 May 2012, 08:38
At bunuel,
A. x<{3} > y= x + 3 +4x =x3+4x=2x+1, which means that when x is in the range {infinity,3} the value of y is defined by x (we would have multiple choices of y depending on x from the given range);
B. 3\leq{x}\leq{4} > y=x+3+4x=x+3+4x=7, which means that when x is in the range {3,4} the value of y is 7 (value of y does not depend on value of x, when x is from the given range);
C. x>{4} > y=x+3+4x=x+34+x=2x1, which means that when x is in the range {4, +infinity} the value of y is defined by x (we would have multiple choices of y depending on x from the given range).
I understand the how you got the check points 3 and 4 but I am having a hard time understanding how to decide sign for x when you are removing absolute value symbol for example for (A) x<3 y= x + 3 +4x how did you decide sign of "x" here ===> x3+4x 2x+1
Similarly can u also explain for (B) and (C)
thank you!
K



Math Expert
Joined: 02 Sep 2009
Posts: 44399

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
28 May 2012, 05:23
kartik222 wrote: At bunuel,
A. x<{3} > y= x + 3 +4x =x3+4x=2x+1, which means that when x is in the range {infinity,3} the value of y is defined by x (we would have multiple choices of y depending on x from the given range);
B. 3\leq{x}\leq{4} > y=x+3+4x=x+3+4x=7, which means that when x is in the range {3,4} the value of y is 7 (value of y does not depend on value of x, when x is from the given range);
C. x>{4} > y=x+3+4x=x+34+x=2x1, which means that when x is in the range {4, +infinity} the value of y is defined by x (we would have multiple choices of y depending on x from the given range).
I understand the how you got the check points 3 and 4 but I am having a hard time understanding how to decide sign for x when you are removing absolute value symbol for example for (A) x<3 y= x + 3 +4x how did you decide sign of "x" here ===> x3+4x 2x+1
Similarly can u also explain for (B) and (C)
thank you!
K Absolute value properties:When \(x\leq{0}\) then \(x=x\), or more generally when \(some \ expression\leq{0}\) then \(some \ expression\leq{(some \ expression)}\). For example: \(5=5=(5)\); When \(x\geq{0}\) then \(x=x\), or more generally when \(some \ expression\geq{0}\) then \(some \ expression\leq{some \ expression}\). For example: \(5=5\); So, for example if \(x<3\) then \(x+3<0\) and \(4x>0\) which means that \(x+3=(x+3)\) and \(4x=4x\) > \(x+3+4x=(x+3)+4x=2x+1\). Similarly for B and C. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 02 Jun 2011
Posts: 143

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
28 May 2012, 09:10
Bunuel wrote: thirst4edu wrote: If x & y are integers and y=x+3 + 4x, does y equals 7? 1) x < 4 2) x > 3 Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks. OA is \(y=x+3+4x\) two check points: \(x=3\) and \(x=4\) (check point: the value of \(x\) when expression in  equals to zero), hence three ranges to consider: A. \(x<{3}\) > \(y= x + 3 +4x =x3+4x=2x+1\), which means that when \(x\) is in the range {infinity,3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range); B. \(3\leq{x}\leq{4}\) > \(y=x+3+4x=x+3+4x=7\), which means that when \(x\) is in the range {3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range); C. \(x>{4}\) > \(y=x+3+4x=x+34+x=2x1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range). Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {3,4} (1) \(x<4\) > not sufficient (\(x<4\) but we don't know if it's \(\geq{3}\)); (2) \(x>3\) > not sufficient (\(x>3\) but we don't know if it's \(\leq{4}\)); (1)+(2) \(3<x<4\) exactly the range we needed, so \(y=7\). Sufficient. Answer: C. OR: looking at \(y=x+3+4x\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4x\) are both positive, in this case \(xes\) cancel out each other and we would have \(y=x+3+4x=x+3+4x=7\). Both \(x+3\) and \(4x\) are positive in the range \(3<{x}<4\) (\(x+3>0\) > \(x>3\) and \(4x>0\) > \(x<4\)). Hope it's clear. inequalities are posing problems!  one doubt  when it is said "3<x<4", in this range shouldn't we check 2, 1 or 2,1 etc and see what is the value for y? is y independent of x when x<0?



Manager
Joined: 12 May 2012
Posts: 78
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25 GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
01 Jun 2012, 05:36
Bunuel wrote: thirst4edu wrote: If x & y are integers and y=x+3 + 4x, does y equals 7? 1) x < 4 2) x > 3 Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks. OA is \(y=x+3+4x\) two check points: \(x=3\) and \(x=4\) (check point: the value of \(x\) when expression in  equals to zero), hence three ranges to consider: A. \(x<{3}\) > \(y= x + 3 +4x =x3+4x=2x+1\), which means that when \(x\) is in the range {infinity,3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range); B. \(3\leq{x}\leq{4}\) > \(y=x+3+4x=x+3+4x=7\), which means that when \(x\) is in the range {3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range); C. \(x>{4}\) > \(y=x+3+4x=x+34+x=2x1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range). Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {3,4} (1) \(x<4\) > not sufficient (\(x<4\) but we don't know if it's \(\geq{3}\)); (2) \(x>3\) > not sufficient (\(x>3\) but we don't know if it's \(\leq{4}\)); (1)+(2) \(3<x<4\) exactly the range we needed, so \(y=7\). Sufficient. Answer: C. OR: looking at \(y=x+3+4x\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4x\) are both positive, in this case \(xes\) cancel out each other and we would have \(y=x+3+4x=x+3+4x=7\). Both \(x+3\) and \(4x\) are positive in the range \(3<{x}<4\) (\(x+3>0\) > \(x>3\) and \(4x>0\) > \(x<4\)). Hope it's clear. MOD questions always floor me. Could you please suggest some good material on MODs?



Math Expert
Joined: 02 Sep 2009
Posts: 44399

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
01 Jun 2012, 07:37
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



Manager
Joined: 24 Mar 2010
Posts: 76

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
20 Dec 2012, 09:01
1
This post received KUDOS
2
This post was BOOKMARKED
Thinking of modulus as distances x+3 => distance of x from 3 x4 => distance of x from 4 Picture the same on the number line ________3_____________0_________________4__________ We are given that y is the sum of the distance of x from 3 & of x from 4 Hence y could be anywhere on the number line For y=7, let us consider the possibilities Case (1) _____x______3_____________0_________________4__________ As you can quickly conclude Its impossible for the distance to be 7 if x < 3 Take x = 4 and check, y = 1 + 8 = 9 Case (2) _________3_____________0_________________4_____x_____ As you can quickly conclude Its impossible for the distance to be 7 if x >4 Take x = 5 and check, y = 8 + 1 = 9 Hence the range for y = 7 has to be in third case __3_____________x_________________4_____ i.e. 3<x<4 So we need to find if 3<x<4 ???? (1) x < 4 Insuff (2) x > 3 Insuff (3) Combining  3<x<4 Bangon. Hence C
_________________
 Stay Hungry, stay Foolish 



Manager
Joined: 12 Dec 2012
Posts: 225
Concentration: Leadership, Marketing
GMAT 1: 540 Q36 V28 GMAT 2: 550 Q39 V27 GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
27 Mar 2013, 07:58
Bunuel wrote: thirst4edu wrote: If x & y are integers and y=x+3 + 4x, does y equals 7? 1) x < 4 2) x > 3 Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks. OA is \(y=x+3+4x\) two check points: \(x=3\) and \(x=4\) (check point: the value of \(x\) when expression in  equals to zero), hence three ranges to consider: A. \(x<{3}\) > \(y= x + 3 +4x =x3+4x=2x+1\), which means that when \(x\) is in the range {infinity,3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range); B. \(3\leq{x}\leq{4}\) > \(y=x+3+4x=x+3+4x=7\), which means that when \(x\) is in the range {3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range); C. \(x>{4}\) > \(y=x+3+4x=x+34+x=2x1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range). Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {3,4} (1) \(x<4\) > not sufficient (\(x<4\) but we don't know if it's \(\geq{3}\)); (2) \(x>3\) > not sufficient (\(x>3\) but we don't know if it's \(\leq{4}\)); (1)+(2) \(3<x<4\) exactly the range we needed, so \(y=7\). Sufficient. Answer: C. OR: looking at \(y=x+3+4x\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4x\) are both positive, in this case \(xes\) cancel out each other and we would have \(y=x+3+4x=x+3+4x=7\). Both \(x+3\) and \(4x\) are positive in the range \(3<{x}<4\) (\(x+3>0\) > \(x>3\) and \(4x>0\) > \(x<4\)). Hope it's clear. Thanks for the great explanation . I got this answer when I tackled it using the same approach .. but got an E when I tried to tackle it in the +/ (x+3)=+/(4x) . I found y = +7 , 7 , 2x1 , 2x+1 , and on plugging values that satisfy the 2 statements together it turned out to a range of 5 to 5 . Could you please guide ? Thanks a million
_________________
My RC Recipe http://gmatclub.com/forum/thercrecipe149577.html
My Problem Takeaway Template http://gmatclub.com/forum/thesimplestproblemtakeawaytemplate150646.html



Math Expert
Joined: 02 Sep 2009
Posts: 44399

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
27 Mar 2013, 09:02
TheNona wrote: Bunuel wrote: thirst4edu wrote: If x & y are integers and y=x+3 + 4x, does y equals 7? 1) x < 4 2) x > 3 Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks. OA is \(y=x+3+4x\) two check points: \(x=3\) and \(x=4\) (check point: the value of \(x\) when expression in  equals to zero), hence three ranges to consider: A. \(x<{3}\) > \(y= x + 3 +4x =x3+4x=2x+1\), which means that when \(x\) is in the range {infinity,3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range); B. \(3\leq{x}\leq{4}\) > \(y=x+3+4x=x+3+4x=7\), which means that when \(x\) is in the range {3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range); C. \(x>{4}\) > \(y=x+3+4x=x+34+x=2x1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range). Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {3,4} (1) \(x<4\) > not sufficient (\(x<4\) but we don't know if it's \(\geq{3}\)); (2) \(x>3\) > not sufficient (\(x>3\) but we don't know if it's \(\leq{4}\)); (1)+(2) \(3<x<4\) exactly the range we needed, so \(y=7\). Sufficient. Answer: C. OR: looking at \(y=x+3+4x\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4x\) are both positive, in this case \(xes\) cancel out each other and we would have \(y=x+3+4x=x+3+4x=7\). Both \(x+3\) and \(4x\) are positive in the range \(3<{x}<4\) (\(x+3>0\) > \(x>3\) and \(4x>0\) > \(x<4\)). Hope it's clear. Thanks for the great explanation . I got this answer when I tackled it using the same approach .. but got an E when I tried to tackle it in the +/ (x+3)=+/(4x) . I found y = +7 , 7 , 2x1 , 2x+1 , and on plugging values that satisfy the 2 statements together it turned out to a range of 5 to 5 . Could you please guide ? Thanks a million Could you please elaborate the red part?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 12 Dec 2012
Posts: 225
Concentration: Leadership, Marketing
GMAT 1: 540 Q36 V28 GMAT 2: 550 Q39 V27 GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
27 Mar 2013, 09:37
Bunuel wrote: Could you please elaborate the red part? I mean that combining both statements x is between 3 and 4 , so I plugged all the values in this range in both 2x1 and 2x+1 giving the range of Ys 5 to 5
_________________
My RC Recipe http://gmatclub.com/forum/thercrecipe149577.html
My Problem Takeaway Template http://gmatclub.com/forum/thesimplestproblemtakeawaytemplate150646.html



Math Expert
Joined: 02 Sep 2009
Posts: 44399

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
28 Mar 2013, 11:42



Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 85
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)

Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7? [#permalink]
Show Tags
07 May 2013, 21:08
mario1987 wrote: Hi guys, I would like to deeply understand how to deal with absolute value questions like the one attached. Thank you very much The Expression given in the Question is Y = lx+3l + l4xl .. & Question asks Is Y = 7 ???? Statement 1 :: x<4 ..... when we plugin any value of x less than 4 till 3 we will get a result as Y = 7 but below 3 ... Y will not be equal to 7 . Therefore, Insufficient. Similarly, Statement :: 2 .... is insufficient....... with 1+2 ..... we get the value of x in between 4 & 3 ...... i.e., 3<x<4 ....... For all the value of x in between 3 & 4 ... the value of Y is always. 7 .. Therefore, Sufficient.... Hence, C ...........
_________________
If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.




Re: If x and y are integers and y = x + 3 + 4  x, does y equals 7?
[#permalink]
07 May 2013, 21:08



Go to page
1 2
Next
[ 27 posts ]



